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Theorem tpcomb 4690
Description: Swap 2nd and 3rd members of an unordered triple. (Contributed by NM, 22-May-2015.)
Assertion
Ref Expression
tpcomb {𝐴, 𝐵, 𝐶} = {𝐴, 𝐶, 𝐵}

Proof of Theorem tpcomb
StepHypRef Expression
1 tpcoma 4689 . 2 {𝐵, 𝐶, 𝐴} = {𝐶, 𝐵, 𝐴}
2 tprot 4688 . 2 {𝐴, 𝐵, 𝐶} = {𝐵, 𝐶, 𝐴}
3 tprot 4688 . 2 {𝐴, 𝐶, 𝐵} = {𝐶, 𝐵, 𝐴}
41, 2, 33eqtr4i 2857 1 {𝐴, 𝐵, 𝐶} = {𝐴, 𝐶, 𝐵}
Colors of variables: wff setvar class
Syntax hints:   = wceq 1536  {ctp 4574
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1969  ax-7 2014  ax-8 2115  ax-9 2123  ax-10 2144  ax-11 2160  ax-12 2176  ax-ext 2796
This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-3or 1084  df-tru 1539  df-ex 1780  df-nf 1784  df-sb 2069  df-clab 2803  df-cleq 2817  df-clel 2896  df-nfc 2966  df-v 3499  df-un 3944  df-sn 4571  df-pr 4573  df-tp 4575
This theorem is referenced by:  f13dfv  7034  frgr3v  28057  signswch  31835  signstfvcl  31847  dvh4dimN  38587
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